Level Of Mean-field Theory Research Articles

Driven-Dissipative Criticality within the Discrete Truncated Wigner Approximation.

We present an approach to the numerical simulation of open quantum many-body systems based on the semiclassical framework of the discrete truncated Wigner approximation. We establish a quantum jump formalism to integrate the quantum master equation describing the dynamics of the system, which we find to be exact in both the noninteracting limit and the limit where the system is described by classical rate equations. We apply our method to simulation of the paradigmatic dissipative Ising model, where we are able to capture the critical fluctuations of the system beyond the level of mean-field theory.

Morphology of an Interacting Three-Dimensional Trapped Bose–Einstein Condensate from Many-Particle Variance Anisotropy

The variance of the position operator is associated with how wide or narrow a wave-packet is, the momentum variance is similarly correlated with the size of a wave-packet in momentum space, and the angular-momentum variance quantifies to what extent a wave-packet is non-spherically symmetric. We examine an interacting three-dimensional trapped Bose–Einstein condensate at the limit of an infinite number of particles, and investigate its position, momentum, and angular-momentum anisotropies. Computing the variances of the three Cartesian components of the position, momentum, and angular-momentum operators we present simple scenarios where the anisotropy of a Bose–Einstein condensate is different at the many-body and mean-field levels of theory, despite having the same many-body and mean-field densities per particle. This suggests a way to classify correlations via the morphology of 100% condensed bosons in a three-dimensional trap at the limit of an infinite number of particles. Implications are briefly discussed.

Variance of a Trapped Bose-Einstein Condensate

The ground state of a Bose-Einstein condensate in a two-dimensional trap potential is analyzed numerically at the infinite-particle limit. It is shown that the anisotropy of the many-particle position variance along the x and y axes can be opposite when computed at the many-body and mean-field levels of theory. This is despite the system being 100% condensed, and the respective energies per particle and densities per particle to coincide.

A Pedagogical Introduction to the Lifshitz Regime

We give an elementary and pedagogical review of the phase diagrams which are possible in quantum chromodynamics (QCD). Herein, emphasis is upon the appearance of a critical endpoint, where disordered and ordered phases meet. In many models, though, a Lifshitz point also arises. At a Lifshitz point, three phases meet: disordered, ordered, and one in which spatially inhomogeneous phases arise. At the level of mean field theory, the appearance of a Lifshitz point does not dramatically affect the phase diagram. We argue, however, that fluctuations about the Lifshitz point are very strong in the infrared and significantly alter the phase diagram. We discuss at length the analogy to inhomogeneous polymers, where the Lifshitz regime produces a bicontinuous microemulsion. We briefly mention the possible relevance to the phase diagram of QCD.

Linear-Response Time-Dependent Embedded Mean-Field Theory.

We present a time-dependent (TD) linear-response description of excited electronic states within the framework of embedded mean-field theory (EMFT). TD-EMFT allows for subsystems to be described at different mean-field levels of theory, enabling straightforward treatment of excited states and transition properties. We provide benchmark demonstrations of TD-EMFT for both local and nonlocal excitations in organic molecules, as well as applications to chlorophyll a, solvatochromic shifts of a dye in solution, and sulfur K-edge X-ray absorption spectroscopy (XAS). It is found that mixed-basis implementations of TD-EMFT lead to substantial errors in terms of transition properties; however, as previously found for ground-state EMFT, these errors are largely eliminated with the use of Fock-matrix corrections. These results indicate that TD-EMFT is a promising method for the efficient, multilevel description of excited-state electronic structure and dynamics in complex systems.

Surface tension of a Yukawa fluid according to mean-field theory.

Yukawa fluids consist of particles that interact through a repulsive or attractive Yukawa potential. A surface tension arises at the walls of the container that encloses the fluid or at the interface between two coexisting phases. We calculate that surface tension on the level of mean-field theory, thereby either ignoring the particle size (ideal Yukawa fluid) or accounting for a non-vanishing particle size through a nonideal contribution to the free energy, exemplified either on the level of a lattice gas (lattice Yukawa fluid) or based on the Carnahan-Starling equation of state (Carnahan-Starling Yukawa fluid). Our mean-field results, which do not rely on assuming small gradients of the particle concentrations, become exact in the limit of large temperature and large screening length. They are calculated numerically in the general case and analytically in the two limits of small particle concentration and close to the critical point for a phase-separating system. For a sufficiently small particle concentration, our predicted surface tension is accurate whereas for a phase boundary, we expect good agreement with exact calculations in the limit of a large screening length and if the mean-field model employs the Carnahan-Starling equation of state.

Order-by-disorder degeneracy lifting of interacting bosons on the dice lattice

Motivated by recent experimental progress in the realization of synthetic gauge fields in systems of ultracold atoms, we consider interacting bosons on the dice lattice with half flux per plaquette. All bands of the non-interacting spectrum of this system were previously found to have the remarkable property of being completely dispersionless. We show that degeneracies remain when interactions are treated at the level of mean field theory, and the ground state exhibits vortex lattice configurations already established in the simpler XY model in the same geometry. We argue that including quantum and thermal fluctuations will select a unique vortex lattice up to overall symmetries based on the order-by-disorder mechanism. We verify the stability of the selected state by analyzing the condensate depletion. The latter is shown to exhibit an unusual non-monotonic behavior as a function of the interaction parameters which can be understood as a consequence of the dispersionless nature of the non-interacting spectrum. Finally, we comment on the role of domain walls which have interactions mediated through fluctuations.

First-Order Disordered-to-Lamellar Phase Transition in Lithium Salt-Doped Block Copolymers.

We study the microphase separation of block copolymer electrolytes containing lithium salts. Taking poly(ethylene oxide)-b-polystyrene (PEO-b-PS) as an example, we show that in the presence of lithium salts the disordered-to-lamellar phase transition becomes first-order even at the level of mean-field theory, with a moderate range of temperature in which both the disordered and lamellar phases coexist, and different salt concentration in the coexisting phases. The coexistence arises from the different partitioning of the salt ions between the disordered phase and the lamellar phase, driven primarily by the solvation energy of anions. A striking consequence of the coexistence is that heating a lamellar phase into the coexistence region leads to increased order in the remaining lamellar phase.

Critical velocity of a clean one-dimensional superconductor

We revisit the problem of critical velocity of a clean one-dimensional superconductor. At the level of mean-field theory, we find that the zero-temperature value of the critical velocity\char22{}the uniform velocity of the superfluid condensate at which the superconducting state becomes unstable\char22{}is a factor of $\sqrt{2}$ smaller than the Landau critical velocity. This is in contrast to a prior finding, which held that the critical velocity is equal to the Landau critical velocity. The smaller value of the critical velocity, which our analysis yields, is the result of a pre-emptive Clogston-Chandrasekhar-type discontinuous phase transition, and is an analog of the threshold value of the uniform exchange field of a superconductor previously investigated by Sarma [J. Phys. Chem. Solids 24, 1029 (1963)] and by Maki and Tsuneto [Prog. Theor. Phys. 31, 945 (1964)]. We also consider the impact of nonzero temperature, study critical currents, and examine metastability and its limits in the temperature versus flow-velocity phase diagram. In addition, we comment on the effects of electron scattering by impurities.

Counter-ion condensation and Kosterlitz–Thouless transition

The similarity between counter-ion condensations in polyelectrolyte rod systems andKosterlitz–Thouless phase transitions in two-dimensional systems is discussed at the levelof mean-field theory. Based on the similarity, the renormalization group theory is applied topolyelectrolyte liquid systems aligned in parallel. It is found that the critical separationbetween monovalent charges for the counter-ion condensation is renormalized inpolyelectrolyte liquid systems and becomes shorter than the Bjerrum length which is thecritical separation predicted by the mean-field theory for a dilute solution of polyelectrolyterods.

Semimicroscopic theory of elasticity near the vulcanization transition

Randomly cross-linked macromolecules undergo a liquid to amorphous-solid phase transition at a critical cross-link concentration. This transition has two main signatures: the random localization of a fraction of the monomers and the emergence of a nonzero static shear modulus. In this paper, a semimicroscopic statistical mechanical theory of the elastic properties of the amorphous solid state is developed. This theory takes into account both quenched disorder and thermal fluctuations, and allows for the direct computation of the free energy change of the sample due to a given macroscopic shear strain. This leads to an unambiguous determination of the static shear modulus. At the level of mean field theory, it is found (i) that the shear modulus grows continuously from zero at the transition, and does so with the classical exponent, i.e., with the third power of the excess cross-link density and, quite surprisingly, (ii) that near the transition the external stresses do not spoil the spherical symmetry of the localization clouds of the particles.

Density functional theory of the inhomogeneous Bose-Einstein condensate

I present a new bosonic density functional especially conceived for the alkali atom Bose gas, together with the corresponding Kohn-Sham equation. The new formalism provides the simplest theory of the observed inhomogeneous Bose-Einstein condensate, beyond the level of mean-field theory.

Fluctuation effects on microphase separation in a random copolymer Hamiltonian

We investigate the effect of fluctuations in the effective Hamiltonian that describes the microphase separation in random copolymers. This Hamiltonian is previously studied on the level of mean-field theory where a phase transition to a phase with periodic microdomain structure was predicted. It is shown that the one-loop treatment of fluctuations is exact in the thermodynamic limit and that the phase predicted by the mean field is unstable within the framework of the studied Hamiltonian.

Phase transitions in heteropolymers with "secondary structure"

We study a model of a random heteropolymer with ``secondary structure'' at the level of mean field theory. The randomness in the polymer sequence is represented by a set of quenched disorder variables that describe the monomer-monomer interactions. The secondary structure is represented by a set of Ising-like thermodynamic variables that describe internal states of the monomers. The interactions between the monomers depend on the quenched disorder variables, on the thermodynamic secondary-structure state variables, and also on the polymer configuration. We find that the system can exist in different phases that depend on the heterogeneity and average strength of the interactions, and on the polymer flexibility. At high temperatures the polymer interconverts freely between configurations without a stable secondary structure. At intermediate temperatures there is a transition to phases with one or two (coexisting) stable secondary-structure motifs and with a large number of thermodynamically important spatial configurations. At low enough temperatures (determined by the polymer flexibility) the polymer undergoes a freezing transition into phases with a unique spatial configuration and one or two stable secondary-structure motifs.

The integral quantum hall effect: Shortcomings of conventional localization theory

Abstract The localization problem in strong magnetic fields, if forced into the mold of conventional perturbation theory, leads to fundamental difficulties. These difficulties already appear on the level of mean field theory.

Instability of the Edwards-Anderson order parameter for an Ising spin glass

The authors make a diagrammatic expansion, without the use of the replica method and at the level of mean-field theory, for the Edwards-Anderson order parameter q, the order parameter susceptibility D, and the spin susceptibility C. The order parameter susceptibility D, which is defined as a positive quantity, is negative below the spin glass freezing temperature. This indicates the instability of the order parameter q.